Answer:
-2+4i
Step-by-step explanation:
Simplify by combining the real and imaginary parts of each expression.
The simplified form of the complex expression is -2 + 4i.
What are Complex Numbers?Complex numbers are numbers which are of the form [tex]a+ib[/tex],
where a and b are real numbers and i is the imaginary number called iota whose value is [tex]i^{2}[/tex] = -1.
Given expression is (2 + 3i) + (-4 + i).
Addition of complex numbers is defined as,
(a + ib) + (a' + ib') = (a + a') + i(b + b')
Using the definition of addition of complex numbers, given expression can be added as,
(2 + 3i) + (-4 + i) = (2 + -4) + i(3 + 1) = -2 + 4i
Hence the resulting value is -2 + 4i.
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Please help math experts thank you
Answer:
.33333 or rounded .33
Step-by-step explanation:
There are 4 months that end in an r
This means that 1 third of the months end in r or .33
60 PTSA grocery store finds that the number of boxes of a new cereal sold increases each week. In the 1st week, 26 boxes of the cereal were sold. In the 2nd week, 58 boxes of the cereal were sold and in the 3rd week 90 boxes of the cereal were sold. The number of boxes of cereal sold each week represents an arithmetic sequence.
Show all work!
A) State the explicit rule for the arithmetic sequence that defines the number of boxes of cereal sold in week n.
B) Use this rule to calculate how many boxes of cereal will be sold during the 9th week.
Answer:
aₙ = 31n - 5
Step-by-step explanation:
The terms of your sequence are.
26, 57, 88, …
This is an arithmetic sequence, because there is a constant difference of 31 between consecutive terms.
The explicit formula for the nth term of an arithmetic sequence is
aₙ = a₁ + d(n - 1 )
a₁ is the first term, and d is the difference in value between consecutive terms. Thus,
aₙ = 26 + 31(n - 1) = 26 + 31n - 31
aₙ = 31n - 5
The explicit rule for the arithmetic sequence is aₙ = 31n - 5.
B. Find the perimeter of the garden when the width is
8 feet.
Answer:
10 - 16
Step-by-step explanation:
My grandmother’s cookie recipe uses 4 cups of sugar to make 35 cookies. My Uncle’s cookie recipe uses 3 cups of sugar to make 28 cookies. Whose cookies are sweeter?
Grandma's
Uncle's
Answer:
uncle's cookies
Step-by-step explanation:
Answer:
I think ur answer would be uncle cookies
Step-by-step explanation:
srry if wrong
hope this helps!
GEOMETRY - triangle similarity
Answer:
ΔABC ≈ ΔDEF
∡B ≅ ∡E
x = 4.5
BC is similar to EF
Step-by-step explanation:
to find 'x':
6/16 = x/12
16x = 72
x = 4.5
Answer:
1) tri ABC ~ tri DEF
2) angle B ~ angle E
3) x= 4.5
4) ?= BC
Step-by-step explanation:
hi! a note: pls let me know if any of the answers are wrong ! i want anyone to have a wrong answer because of me thank u vm! (obviously, my explanations are not the official mathematical explanations)
1) I just matched up the letters, A to D, B to E, C to F
You can also use ratios, but if you dont need an explanation then ignore it.
2) matched up the angles: B corresponds to E
3) Ratio: 6/16 = x/12
16x = 72 cross multiply
x = 4.5
4) Again, just match up the sides
BC corresponds to EF
hope this helps :D best of luck
Can someone help me with this problem?
Answer:
a) 2
b) 3
c) 1
hope this helps :)
Determine the discriminant and then state how many solutions there are and the nature of the solutions. Do not solve. 6x^2-x-2=0
Given:
The quadratic equation is:
[tex]6x^2-x-2=0[/tex]
To find:
The nature of the solutions by using the discriminant.
Solution:
If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then its discriminant is:
[tex]D=b^2-4ac[/tex]
If D<0, then both roots are complex.
If D=0, then both roots are real and equal.
If D>0, then both roots are real and distinct.
We have,
[tex]6x^2-x-2=0[/tex]
Here, [tex]a=6,b=-1,c=-2[/tex]. So, the value of the discriminant is:
[tex]D=(-1)^2-4(6)(-2)[/tex]
[tex]D=1+48[/tex]
[tex]D=49[/tex]
Since [tex]D>0[/tex], then both roots are real and distinct.
Hence, the discriminant of the given quadratic equation is 49 and both roots are real and distinct.
y is directly proportional to x^3
y = 17
when
x = 4
Work out an equation connecting y and x.
Answer:
[tex] 64y = 17 {x}^{3} [/tex]
Step-by-step explanation:
[tex]y \: \alpha \: {x}^{3} ....(given) \\ \therefore \: y = k {x}^{3} .. (1)\\ (k =arbitrary \:constant) \\when \: x = 4, \: \: y = 17, \:k =? \\ 17 = k {(4)}^{3} \\ 17 = 64k \\ k = \frac{17}{64} \\ plug \: k =\frac{17}{64} \: in \: equation \: (1) \\ y = \frac{17}{64} {x}^{3} \\ 64y = 17 {x}^{3} [/tex]
The correct equation connecting y and x is,
⇒ y = 17/64x
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
⇒ y is directly proportional to x³
Hence, We get;
⇒ y = kx³
Here, y 17 at x = 4;
Hence,
⇒ 17 = k × 4³
⇒ k = 17 / 64
Thus, The correct equation connecting y and x is,
⇒ y = 17/64x
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need help will give brainliest
Answer:
40.56
Step-by-step explanation:
2pir
8÷2=r=4
2pi4=25.13
25.13÷2=12.565
10+10+8+12.56=40.565
While mike was visiting his sister in arlington,he bought an aquarium that was marked down 60% from an original price of $100 .if the sales tax in Arlington is 5% ,what was the total cost of the arquarium?
Answer:
The cost of the aquarium was $38
Step-by-step explanation:
I got 60% of 100 and it was 60 so it was $40 but then the sales tax was $2 so I subtracted and got 38
The total cost of the aquarium is the sum of the marked down price and
the sales tax.
The total cost of the aquarium is $42
Reasons:
The known information are;
Original price of the aquarium = $100
The marked down percentage of the aquarium = 60%
The sales tax = 5%
[tex]Mark \ down = \dfrac{Difference}{Current \ selling \ price} \times 100[/tex]
[tex]60 \% = \dfrac{Difference}{100} \times 100[/tex]
Which gives;
The difference in sale = $100 - Marked down price = $60
Marked down price = $100 - $60 = $40
The marked down price = $40
The tax is applied to the marked down price, therefore, we get;
Sales tax = 5% × $40 = $2
The total cost = Marked down price + Sales tax
The total cost of the aquarium = $40 + $2 = $42
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In a quiz , team A scored 2 ,4 , -2 , 0 , -2 team B scored -4 ,2 , 2 ,-2 ,4 in successive5 rounds
.Which team scored more and by how much?
Please help
Answer:
a. 2 b. 2
Step-by-step explanation:
which equation represents that relationship ??
Answer:
A
Step-by-step explanation:
A proportional relationship either increases or decreases its points at the same rate. In the first set of ordered pairs, the x values all increase by 3 while the y values all increase by 6, which is twice the value of the x values' increasing. The second set of ordered pairs is not proportional because all pairs' x values increase by 2 while the y values increase by 8 until ordered pair (5, 20), so this set therefore is non-proportional. y = x + 3 is the correct equation because it represents that the y value is always 3 greater than the x value. All the shown ordered pairs for set 1 supports this (3 - 0 = 3, 6 - 3 = 3, 9 - 6 = 3, 12 - 9 = 3).
which shows the solution in the inequality? -2x > 18
A. x >9
B. x<-9
C. x>-9
D.x<9
HELP PLEASE
Answer: x<-9
Step-by-step explanation:
-2x>18
-2x/(-2)<18/(-2)
x< -9
The value of the solution in the inequality is,
⇒ x < - 9
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
We have to given that;
The inequality is,
⇒ - 2x > 18
Now, We can simplify as;
⇒ - 2x > 18
⇒ - x > 18/2
⇒ - x > 9
⇒ x < - 9
Thus, The value of the solution in the inequality is,
⇒ x < - 9
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Which of the following correctly gives the center and radius of the circle defined by the equation (x - 7)2 + (x - 2)2 = 10? A. Center: (7, 2); Radius = 100 B. Center: (7, 2); Radius = 10 C. Center: (-7, -2); Radius = 100 D. Center: (-7, -2); Radius = 10
Answer:
Center (7,2) and radius = 10
Step-by-step explanation:
Generally, we have the equation of a circle as follows;
(x-a)^2 + (y-b)^2 = r^2
where (a,b) represents the circle center and r represents the radius of the circle
Looking at the given equation of a circle, we have it that the center is (7,2) while the radius of the circle is 10
Can somebody plz help me out:)))
Answer:28 possibly? I know that you connect it with the angles use across from the angle I hope I helped a little
Step-by-step explanation:
Answer:
Sin 30°
= 0.5 appromaxit
Solve for x ax-bx/x+c = d, if a =/b+d
Answer:
dc/a-b-d
Step-by-step explanation:
ax – bx = d
x + c
Multiply both sides by x + c
ax – bx
(x + c) = d(x + c)
x + c
Simplify
ax – bx
(x+c): ax – bx
x + c
ax – bx = d(x+c)
Expand d(x+c): dx + cd
ax — bx = dx + cd
Subtract dx from both sides
ax – bx – dx = dx + cd – dx
Simplify
ax – bx – dx = cd
Factor ax – bx – dx: x(a – b – d)
x(a - b- d) = cd
Divide both sides by a – b – d; a + b + d
x(a – b - d) cd
a + b + d
a - b - d
a – b-d
Simplify
X =dc/a-b-d
The value of 'x' in the algebraic equation is [tex]\rm x= \frac{dc}{a-b-d} \\[/tex] where [tex]\rm a\neq b+d[/tex]
It is given that the algebraic equation [tex]\rm \frac{ax-bx}{x+c}= d[/tex]
It is required to solve the algebraic (polynomial) equation if [tex]\rm a\neq b+d[/tex]
What is polynomial?Polynomial is the combination of variables and constants in a systematic manner with "n" number of power in ascending or descending order.
We have an algebraic equation:
[tex]\rm \frac{ax-bx}{x+c}= d[/tex]
[tex]\rm \frac{ax-bx}{x+c}= d\\\\\rm ax-bx=d(x+c)\\\rm ax-bx=dx+dc\\\rm ax-bx-dx=dc\\\rm (a-b-d)x=dc\\\\\rm x= \frac{dc}{a-b-d} \\[/tex]
Thus, the value of 'x' in the algebraic equation is [tex]\rm x= \frac{dc}{a-b-d} \\[/tex] where [tex]\rm a\neq b+d[/tex]
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Please help quick! I’ll give brainluilyst just please help me
Find the length of side x in simplest radical form with a rational denominator.
45
X
45
V8
Answer:
relationship between perpendicular and hypotenuse is given by sin angle
sin45=p/h
sin45=√8/x
1/√2=√8/x
x=2√2×√2=2×2=4
x=4
I need helppppppppppppp please
Answer:
I want to say A)
Step-by-step explanation:
The hot tub is shaped like a rectangular prism. It is 7 feet long, 3 1/4 feet deep, and has a volume of 159 1/4 cubic feet. What is the width of the hot tub?
Answer:
w = 7 feet
Step-by-step explanation:
Volume of a rectangle prism = length × width × height
Length = 7 feet
Width = ?
Height = 3 1/4 feet
Volume = 159 1/4 cubic feet
Volume of a rectangle prism = length × width × height
159 1/4 = 7 × w × 3 1/4
637/4 = 7 × w × 13/4
637/4 = 7 × 13/4 × w
637/4 = 91/4w
w = 637/4 ÷ 91/4
= 637/4 × 4/91
= 637*4 / 4*91
= 2548 / 364
w = 7 feet
Of the players on a bowling team7/10 or 7 won trophies. Explain how you can find the number of players on the team.?
Answer:
10players
Step-by-step explanation:
Using the concept of probability
probability = expected outcome/total outcome
Total outcome s the numbers of players on the team
Given
Total number of trophy won = 7 (expected)
Fraction of those that won = 7/10 (probability)
Substitute
7/10 = 7/total outcome
1/10 = 1/total outcome
Reciprocate both sides
10/1 = total outcome
Swap
Total outcome = 10
Hence the number of players on the team is 10players
I'll give you brainiest if you help me.
Answer:
88 degrees.
Step-by-step explanation:
Since AB is equal to BC, ABC is an isosceles triangle. Therefore, the angle of B will be 180-39-39=102 degrees. As the angle of a straight line is 180 degrees, take 180-102-32=46 degrees. This 46 degrees is angle B. Since DEB is an isosceles triangle, 180-46-46=88 degrees. 88 degrees is angle E which is your answer. Edit: (Just added on the explanation.)
FIRST CORRECT ANSWER GETS BRANLIEST PLEASE HELP!!!! PHOTO ABOVE
Answer:
Step-by-step explanation:
The Pythagorean theorem is that (for right triangles)
a^2+b^2=c
Meaning c is the side opposite the right angle
Hope this helps!
3 times a number is 4 less than the square of that number. Find the negative solution.
How do you break apart the factor 627 using place value?
Answer:
6 hundreds
2 tens
7 ones
Step-by-step explanation:
Un albañil construye una casa en 5 días si debe construir 3 casas cuántos días se demorará
Tom has a 15 pounds bag of cat food. If he feeds his cat 1/4 pound
of food each day. How many days will the 15 pound bag of
cat food last? Show your thinking.
Answer:
it will take his cat 60 days to finish the entire bag
Step-by-step explanation:
Find the slope of a line parallel to each given line.
if tan27° =k express the following in terms of k
1. sin 27°
Answer:
) ''You need to consider 200^o = 180^o + 20^o , hence you need to use the next formula to evaluate sin 200^o in terms of k:
sin (alpha + beta) = sin alpha*cos beta + sin beta*cos alpha
Plugging alpha = 180^o , beta = 20^o in the formula yields:
sin 200^o = sin (180^o + 20^o) = sin 180^o*cos20^o + sin 20^o*cos 180^o
Plugging sin 180^o = 0 and cos180^o = -1 in the formula yields:
sin 200^o = - sin 20^o = -k''
Step-by-step explanation:
''Given sin 20°=k express the following in terms of k a) sin 200° b) cos 20° c) tan(-20°) d) sin 70° Related to trigonometry.'' https://www.enotes.com/homework-help/given-sin-20-k-express-following-terms-k-sin-200-b-307263 hope this helps
need help no bots those guys r so annoying
Answer:
AC = 16
KL = 5.625
Source(s):
Dude trust me
brainliest tho??
Step-by-step explanation:
5/KL = 12/13.5
12KL = 67.5
KL = 5.625
AC/18 = 12/13.5
13.5AC = 216
AC = 16
Find f-1(x) if f(x) = 2x/3-4
Given:
The function is:
[tex]f(x)=\dfrac{2x}{3}-4[/tex]
To find:
The inverse of the given function, i.e., [tex]f^{-1}(x)[/tex].
Solution:
We have,
[tex]f(x)=\dfrac{2x}{3}-4[/tex]
Step 1: Substitute [tex]f(x)=y[/tex].
[tex]y=\dfrac{2x}{3}-4[/tex]
Step 2: Interchange x and y.
[tex]x=\dfrac{2y}{3}-4[/tex]
Step 3: Isolate y.
[tex]x+4=\dfrac{2y}{3}[/tex]
[tex]3(x+4)=2y[/tex]
[tex]\dfrac{3x+12}{2}=y[/tex]
[tex]\dfrac{3}{2}x+6=y[/tex]
Step 4: Substitute [tex]y=f^{-1}(x)[/tex].
[tex]f^{-1}(x)=\dfrac{3}{2}x+6[/tex]
Therefore, the inverse of the given function is [tex]f^{-1}(x)=\dfrac{3}{2}x+6[/tex].